Decision Table Based Testing Outline Decision table vocabulary –Limited Entry Decision Tables...

Decision Table Based Testing Outline

• Decision table vocabulary– Limited Entry Decision Tables (LEDT)– Extended Entry Decision Tables (EEDT)– Mixed Entry Decision Tables (MEDT)

• Techniques– Redundant LEDTs– Inconsistent LEDTs

• Examples• Guidelines• Cause and Effect Graphs

Decision Table Based Testing

• Decision table is based on logical relationships just as the truth table.

• Decision Table is a tool that helps us look at the combination of conditions

– Completeness of conditions– Inconsistency of conditions

Decision Table Based Testing

• Originally known as Cause and Effect Graphing– Done with a graphical technique that expressed

AND-OR-NOT logic.– Causes and Effects were graphed like circuit

components– Inputs to a circuit “caused” outputs (effects)

• Equivalent to forming a decision table in which: – inputs are conditions– outputs are actions

• Test every (possible) rule in the decision table.• Recommended for logically complex situations.• Excellent example of Model-Based Testing (MBT)

Content of a Decision Table

• Conditions– binary in a Limited Entry Decision Table– finite set in an Extended Entry Decision Table– condition stub– condition entries

• Actions– also binary, either do or skip– the “impossible” action

• Rules– a rule consists of condition entries and action entries– a complete, non-redundant LEDT with n conditions has 2n rules– logically impossible combinations of conditions are “impossible

rules”, denoted by an entry in the impossible action

Components of a Decision Table

C1

C2

C3

a1

a2

a3

a4

a5

T T T T F F F F

T T F F T T F F

T F T F T F T F

x x x xx x x x

x x x xx x

“binary”conditions

actions

values of conditions

actions taken

R1 R2 R3 R4 R5 R6 R7 R8

rules

Read a Decision Table by columns of rules : (e.g. R1 from reqs. or design says when all conditions are T, then actions a1, a2, and a5 should occur)

Example (continued)

• The condition entries in rules 3 and 4, and rules 7 and 8 have the same actions. The “—” means ...– “Don’t Care” (as in circuit analysis),– Irrelevant, or– not applicable, n/a

Stub Rule 1 Rule 2 Rules 3, 4 Rule 5 Rule 6 Rules 7, 8

c1 T T T F F F

c2 T T F T T F

c3 T F — T F T

a1 X X X —

a2 X X

a3 X

a4 X X X

Example (continued)

Stub Rule 1 Rule 2 Rules 3, 4, 7, 8 Rule 5 Rule 6

c1 T T — F F

c2 T T F T T

c3 T F — T F

a1 X X X

a2 X X

a3 X

a4 X X

count 1 1 4 1 1

• Rule counting– a rule with no don’t care entries counts as 1– each don’t care entry in a rule doubles the rule count– for a table with n limited entry conditions, the sum of the

rule counts should be 2n.

Problematic Decision Tables

• For LEDTs, simple rule counting helps identify decision tables that are ...– incomplete ( rule count < 2n ) , – redundant ( rule count > 2n ) , or– inconsistent

• ( rule count > 2n ) AND• at least two rules have identical condition entries but different action

entries.

• Redundancy and inconsistency are more likely with algebraically simplified tables that have been “maintained”.

A Redundant DT

• Rule 9 is redundant with Rules 1 – 4 (technically, with what was rule 4)

• But the action entries are identical (No harm, no foul?)

conditions 1 – 4 5 6 7 8 9

c1 T F F F F T

c2 — T T F F F

c3 — T F T F F

a1 X X X — — X

a2 — X X X — —

a3 X — X X X X

An Inconsistent DT

• Rule 9 is inconsistent with Rules 1 – 4 (technically, with what was rule 4)– condition portion is identical, BUT– action portion is different

• What happens when Rule 4 is executed? Rule 9?

conditions 1 – 4 5 6 7 8 9

c1 T F F F F T

c2 — T T F F F

c3 — T F T F F

a1 X X X — — —a2 — X X X — Xa3 X — X X X —

Month Equivalence Classes (to be used in the next example)

• M1 ={x : x is a 30-day month}• M2 ={x : x is a 31-day month}• M3 ={x : x is February}

Last Day of Month Decision Tableconditions 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

c1. M1? T T T T T T T T F F F F F F F F

c2. M2? T T T T F F F F T T T T F F F F

c3. M3? T T F F T T F F T T F F T T F F

c4. leap year? T F T F T F T F T F T F T F T F

a1. last day = 30 x x


a3. last day = 28 x

a4. last day = 29 x

a5. impossible x x x x x x x x x x

• Rule pairs 1 and 2, 3 and 4, 5 and 6, 9 and 10 don’t need c4, so they could be combined, BUT

• Impossible because c1, c2, and c3 are mutually exclusive.

Extended Entry Decision Tables

• When conditions are mutually exclusive, exactly one must be true.

• Extended entry decision tables typically (but not necessarily) have mutually exclusive conditions.

• The “extended” part is because a condition stub is an incomplete statement that is completed by the condition entry.

• (See the revised Last Day of Month EEDT)

Revised Last Day of Month DT

• When conditions are mutually exclusive, exactly one must be true.

• This can be further simplified.

c1. 30-day month? M1 M1 — — — —

c2. 31-day month? — — M2 M2 — —

c3. February? — — — — M3 M3

c4. leap year? T F T F T F



a3. last day = 28 x

a4. last day = 29 x

The “Emphatic False”

• Maybe “—” should be replaced by “must be False”• One writer suggested “F!” (before “!” meant “NOT”)• It is a Don’t Care in c4.• Technically, this is a Mixed Entry Decision Table,

because it has both extended and limited entry conditions.

c1. month in M1 — — —

c2. month in — M2 — —

c3. month in — — M3 M3

c4. leap year? — — T F

a1. last day = 30 x

a2. last day = 31 x

a3. last day = 28 x

a4. last day = 29 x

c1: a, b, c form a triangle? F T T T T T T T Tc2: a = b? — T T T T F F F Fc3: a = c? — T T F F T T F Fc4: b = c? — T F T F T F T Fa1: Not a triangle Xa2: Scalene Xa3: Isosceles X X Xa4: Equilateral Xa5: Impossible X X X

Triangle Program Decision Table

Why are some rules impossible?

Expanding c1...c1: a<b+c? F T T T T T T T T T T

c2: b<a+c? — F T T T T T T T T T

c3: c<a+b? — — F T T T T T T T T

c4: a = b? — — — T T T T F F F F

c5: a = c? — — — T T F F T T F F

c6: b = c? — — — T F T F T F T F

a1: Not a triangle x x x

a2: Scalene x

a3: Isosceles x x x

a4: Equilateral x

a5: Impossible x x x

• Is this a complete decision table? How many test cases does this imply?

Triangle Problem Example (“short” form)

1. a < b + c2. b < a + c3. c < a + b

4. a = b5. a = c6. b = c

1. Not triangle

1. Scalene2. Isosceles3. Equilateral4. “impossible”

F T T T T T T T T T T - F T T T T T T T T T- - F T T T T T T T T

- - - T T T T F F F F- - - T T F F T T F F- - - T F T F T F T F

X X X

X X X X X X X X Note the

Impossible cases

Pick input set, <a, b, c>, for each of the columns, or rules, belowAssume a, b and c are

all between 1 and 200 R1 R2 R3 R4 R5 R7R6 R9R8 R11R10

equivalent orall necessary

Req or Design should NOT have these cases

Rule Counting

c1: a<b+c? F T T T T T T T T T T

c2: b<a+c? — F T T T T T T T T T

c3: c<a+b? — — F T T T T T T T T

c4: a = b? — — — T T T T F F F F

c5: a = c? — — — T T F F T T F F

c6: b = c? — — — T F T F T F T F

Rule count 32 16 8 1 1 1 1 1 1 1 1

a1: Not a triangle x x x

a2: Scalene x

a3: Isosceles x x x

a4: Equilateral x

a5: Impossible x x x

Corresponding Test Cases

Case ID a b c Expected Output

DT1 4 1 2 Not a Triangle



DT4 5 5 5 Equilateral

DT5 ? ? ? Impossible


DT7 2 2 3 Isosceles


DT9 2 3 2 Isosceles

DT10 3 2 2 Isosceles

DT11 3 4 5 Scalene

NextDate Decision Table (first half)

1 2 3 4 5 6 7 8 9 10

c1: month in M1 M1 M1 M1 M1 M2 M2 M2 M2 M2

c2: day in D1 D2 D3 D4 D5 D1 D2 D3 D4 D5

c3: year in — — — — — — — — — —

a1: impossible X

a2: increment day X X X X X X X

a3: reset day X X

a4: increment month X X

a5: reset month

a6: increment year

M1: 30 days months, M2: 31 days months, M3: Dec, M4: FebD1: 1~27, D2: 28, D3: 29, D4: 30, D5: 31Y1: leap year, Y2: common year

NextDate Decision Table (first half reduced)

1–3 4 5 6–9 10

c1: month in M1 M1 M1 M2 M2

c2: day in D1, D2, D3 D4 D5 D1, D2, D3, D4 D5

c3: year in — — — — —

a1: impossible X

a2: increment day X X

a3: reset day X X

a4: increment month

X X

a5: reset month

a6: increment year

NextDate Decision Table (second half)

11 12 13 14 15 16 17 18 19 20 21 22

c1: month in M3 M3 M3 M3 M3 M4 M4 M4 M4 M4 M4 M4

c2: day in D1 D2 D3 D4 D5 D1 D2 D2 D3 D3 D4 D5

c3: year in — — — — — — Y1 Y2 Y1 Y2 — —

a1: impossible X X X

a2: increment day X X X X X X

a3: reset day X X X


a5: reset month X

a6: increment year X

M1: 30 days months, M2: 31 days months, M3: Dec, M4: FebD1: 1~27, D2: 28, D3: 29, D4: 30, D5: 31Y1: leap year, Y2: common year

NextDate Decision Table (second half reduced)

11–14 15 16 17 18 19 20 21, 22

c1: month in M3 M3 M4 M4 M4 M4 M4 M4

c2: day in D1, D2, D3, D4

D5 D1 D2 D2 D3 D3 D4, D5

c3: year in — — — Y1 Y2 Y1 Y2 —

a1: impossible X X

a2: increment day X X

a3: reset day X X X X


a5: reset month X

a6: increment year X

NextDate Test CasesTest Case Rule(s) Month Day Year Expected Output

1 1– 3 4 15 2001 4/16/2001

2 4 4 30 2001 5/1/2001

3 5 4 31 2001 Invalid Input Date

4 6–9 1 15 2001 1/16/2001

5 10 1 31 2001 2/1/2001

6 11–14 12 15 2001 12/16/2001

7 15 12 31 2001 1/1/2002

8 16 2 15 2001 2/16/2001

9 17 2 28 2004 2/29/2004

10 18 2 28 2001 3/1/2001

11 19 2 29 2004 3/1/2004

12 20 2 29 2001 Invalid Input Date

13 21, 22 2 30 2001 Invalid Input Date

Advantages/Disadvantages of Decision Table

• Advantages: (check completeness & consistency)1. Allow us to start with a “complete” view, with no

consideration of dependence2. Allow us to look at and consider “dependence,”

“impossible,” and “not relevant” situations and eliminate some test cases.

3. Allow us to detect potential error in our Specifications

• Disadvantages:1. Need to decide (or know) what conditions are

relevant for testing - - - this may require Domain knowledge• e.g. need to know leap year for “next date” problem in

the book2. Scaling up can be massive: 2n rules for n

conditions - - - that’s if the conditions are binary and gets worse if the values are more than binary

Decision Table Based Testing Outline Decision table vocabulary –Limited Entry Decision Tables...

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